Online algorithms for a dual version of bin packing
Discrete Applied Mathematics
An improved lower bound for on-line bin packing algorithms
Information Processing Letters
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
Better approximation algorithms for bin covering
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the online bin packing problem
Journal of the ACM (JACM)
On-line Packing and Covering Problems
Developments from a June 1996 seminar on Online algorithms: the state of the art
An asymptotic fully polynomial time approximation scheme for bin covering
Theoretical Computer Science
An efficient approximation scheme for the one-dimensional bin-packing problem
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Linear time-approximation algorithms for bin packing
Operations Research Letters
Bin packing problems with rejection penalties and their dual problems
Information and Computation
Bin packing problems with rejection penalties and their dual problems
Information and Computation
On-Line Sequential Bin Packing
The Journal of Machine Learning Research
Hi-index | 0.00 |
In this paper we consider the following problems: We are given a set of n items {u1, ⋯, un}, each item ui is characterized by its size wi∈ (0,1] and its penalty/profit pi≥ 0, and a number of unit-capacity bins. An item can be either rejected, in which case we pay/get its penalty/profit, or put into one bin under the constraint that the total size of the items in the bin is not greater/smaller than 1. No item can be spread into more than one bin. The objective is to minimize/maximize the sum of the number of used/covered bins and the penalties/profits of all rejected items. We call the problems bin packing/covering with rejection penalties/profits, and denoted by BPR and BCR respectively. For the online BPR problem, we present an algorithm with an absolute competitive ratio of 2.618 while the lower bound is 2.343, and an algorithm with an asymptotic competitive ratio of arbitrarily close to 7/4 while the lower bound is 1.540. For the offline BPR problem, we present an algorithm with an absolute worst-case ratio of 2 while the lower bound is 3/2, and an algorithm with an asymptotic worst-case ratio of 3/2. For the online BCR problem, we show that no algorithm can have an absolute competitive ratio of greater than 0, and present an algorithm with an asymptotic competitive ratio of 1/2, which is the best possible. For the offline BCR problem, we also present an algorithm with an absolute worst-case ratio of 1/2 which matches the lower bound.